Earth’s gravity gradient and eddy currents effects on the rotational dynamics of space debris objects: Envisat case study

Abstract

The Space Debris population has grown rapidly over the last few decades with the consequent growth of impact risk between current objects in orbit. Active Debris Removal (ADR) has been recommended to be put into practice by several National Agencies in order to remove objects that pose the biggest risk for the space community. The most immediate target that is being considered for ADR by the European Space Agency is the Earth-observing satellite Envisat. In order to safely remove such a massive object from its orbit, a capturing process followed by a controlled reentry is necessary. However, current ADR methods that require physical contact with the target have limitations on the maximum angular momentum that can be absorbed and a de-tumbling phase prior to the capturing process may be required. Therefore, it is of utmost importance for the ADR mission design to be able to predict accurately how the target will be rotating at the time of capture. This article analyses two perturbations that affect an object in Low Earth Orbit (LEO), the Earth's gravity gradient and the eddy currents induced by the Earth's magnetic field. The gravity gradient is analysed using the equation of conservation of total energy and a graphical method is presented to understand the expected behaviour of any object under the effect of this perturbation. The eddy currents are also analysed by studying the total energy of the system. The induced torque and the characteristic time of decay are presented as a function of the object's magnetic tensor. In addition, simulations were carried out for the Envisat spacecraft including the gravity gradient perturbation as well as the eddy currents effect using the International Geomagnetic Reference Field IGRF-11 to model the Earth's magnetic field. These simulations show that the combined effect of these two perturbations is a plausible explanation for the rotational speed decay

Long-term attitude dynamics of space debris in Sun-synchronous orbits: Cassini cycles and chaotic stabilization

“…This assumption holds for rocket bodies, which are the primary target of this study. As in prior research (Gomez and Walker (2015); Lin and Zhao (2015); Praly et al (2012)) when modeling the rotational dynamics with respect to object's center of mass, we shall take into account gravity gradient torque M G and torque due to eddy currents M EC .…”

Concurrent image-based visual servoing with adaptive zooming for non-cooperative rendezvous maneuvers

“…By using Equation 34together with Equations (36) and 37 Agency, because of its mass, size and threat of collisions with other objects in orbit [49]. In order to safely remove such a massive object from its orbit, a system capturing process followed by a controlled reentry maneuver is necessary.…”

Attitude control analysis of tethered de-orbiting

“…The end bodies are connected by a discretized viscous-elastic tether. Based on the attitude motion analysis [18,19] of the inactive Envisat satellite, which is the focus of the e.Deorbit mission [17], a representative ADR mission scenario is considered which accounts for small, residual initial angular rates of the target prior to the deorbit burn. Furthermore, no input shaping of the deorbit burn is used.…”